Jacobi-Gauss-Lobatto collocation method for solving nonlinear reaction-diffusion equations subject to Dirichlet boundary conditions

被引:13
作者
Bhrawy, A. H. [1 ,2 ]
Doha, E. H. [3 ]
Abdelkawy, M. A. [2 ]
Van Gorder, R. A. [4 ]
机构
[1] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia
[2] Beni Suef Univ, Fac Sci, Dept Math, Bani Suwayf, Egypt
[3] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt
[4] Univ Oxford, Math Inst, Radcliffe Observ Quarter, Andrew Wiles Bldg, Oxford OX2 6GG, England
关键词
Nonlinear reaction-diffusion equations; Collocation method; Jacobi-Gauss-Lobatto quadrature; SPECTRAL GALERKIN METHOD; SOLITARY WAVE SOLUTIONS; TANH METHOD; TRAVELING-WAVES; NAGUMO EQUATION; BURGERS-HUXLEY; APPROXIMATION; TIME;
D O I
10.1016/j.apm.2015.09.009
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper extends the application of the spectral Jacobi-Gauss-Lobatto collocation (J-GL-C) method based on Gauss-Lobatto nodes to obtain semi-analytical solutions of nonlinear time dependent reaction-diffusion equations (RDEs) subject to Dirichlet boundary conditions. This approach has the advantage of allowing us to obtain the solution in terms of the Jacobi parameters alpha and beta, which therefore means that the method holds a number of collocation methods as a special case. In addition, the problem is reduced to the solution of system of ordinary differential equations (SODEs) in the time variable, which may then be solved by any standard numerical technique. We consider five applications of the general method to concrete examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving nonlinear time-dependent RDEs. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码:1703 / 1716
页数:14
相关论文
共 51 条
[1]  
[Anonymous], 2013, Mathematical Biology
[2]  
[Anonymous], 1937, B MOSCOW U MATH MECH
[3]  
[Anonymous], 1986, Reaction-diffusion equations and their applications to biology
[4]  
Beals R., 2010, Special Functions
[5]   An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system [J].
Bhrawy, A. H. .
APPLIED MATHEMATICS AND COMPUTATION, 2014, 247 :30-46
[6]   A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations [J].
Bhrawy, A. H. ;
Alofi, A. S. .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2012, 17 (01) :62-70
[7]   A shifted Jacobi-Gauss-Lobatto collocation method for solving nonlinear fractional Langevin equation involving two fractional orders in different intervals [J].
Bhrawy, Ali H. ;
Alghamdi, Mohammed A. .
BOUNDARY VALUE PROBLEMS, 2012,
[8]   A Jacobi Dual-Petrov Galerkin-Jacobi Collocation Method for Solving Korteweg-de Vries Equations [J].
Bhrawy, Ali H. ;
Al-Shomrani, M. M. .
ABSTRACT AND APPLIED ANALYSIS, 2012,
[9]   DIFFUSION IN NONLINEAR MULTIPLICATIVE MEDIA [J].
CANOSA, J .
JOURNAL OF MATHEMATICAL PHYSICS, 1969, 10 (10) :1862-&
[10]  
Canuto C., 2006, SCIENTIF COMPUT, DOI 10.1007/978-3-540-30726-6